Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai, Tamil Nadu, India.
Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, Ostrava, Czechia.
Front Public Health. 2024 Oct 21;12:1398325. doi: 10.3389/fpubh.2024.1398325. eCollection 2024.
This work focuses on the Dengue-viremia ABC (Atangana-Baleanu Caputo) fractional-order differential equations, accounting for both symptomatic and asymptomatic infected cases. Symptomatic cases are characterized by higher viremia levels, whereas asymptomatic cases exhibit lower viremia levels. The fractional-order model highlights memory effects and other advantages over traditional models, offering a more comprehensive representation of dengue dynamics.
The total population is divided into four compartments: susceptible, asymptomatic infected, symptomatic infected, and recovered. The model incorporates an immune-boosting factor for asymptomatic infected individuals and clinical treatment for symptomatic cases. Positivity and boundedness of the model are validated, and both local and global stability analyses are performed. The novel Adams-Bash numerical scheme is utilized for simulations to rigorously assess the impact of optimal control interventions.
The results demonstrate the effectiveness of the proposed control strategies. The reproduction numbers must be reduced based on specific optimal control conditions to effectively mitigate disease outbreaks. Numerical simulations confirm that the optimal control measures can significantly reduce the spread of the disease.
This research advances the understanding of Dengue-viremia dynamics and provides valuable insights into the application of ABC fractional-order analysis. By incorporating immune-boosting and clinical treatment into the model, the study offers practical guidelines for implementing successful disease control strategies. The findings highlight the potential of using optimal control techniques in public health interventions to manage disease outbreaks more effectively.
本研究聚焦于登革热病毒血症 ABC（Atangana-Baleanu Caputo）分数阶微分方程，同时考虑有症状和无症状感染病例。有症状病例的病毒血症水平较高，而无症状病例的病毒血症水平较低。分数阶模型强调了记忆效应和其他优于传统模型的优势，更全面地描述了登革热的动态。
总人群分为四个 compartments：易感者、无症状感染者、有症状感染者和康复者。模型中考虑了无症状感染者的免疫增强因素和有症状病例的临床治疗。验证了模型的正定性和有界性，并进行了局部和全局稳定性分析。采用新颖的 Adams-Bash 数值方案进行模拟，以严格评估最优控制干预的影响。
结果表明所提出的控制策略的有效性。根据特定的最优控制条件，必须降低繁殖数，以有效减轻疾病爆发。数值模拟证实了最优控制措施可以显著减少疾病的传播。
本研究推进了对登革热病毒血症动力学的理解，并为 ABC 分数阶分析的应用提供了有价值的见解。通过将免疫增强和临床治疗纳入模型，该研究为实施成功的疾病控制策略提供了实用的指导方针。研究结果强调了在公共卫生干预中使用最优控制技术来更有效地管理疾病爆发的潜力。
